Degree | Type | Year |
---|---|---|
2503758 Data Engineering | FB | 1 |
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No required.
The subject is structured in four blocks: a first more computational block where the algebraic manipulation of matrices is prioritized, introducing their basic operations. In the second block the concepts of abstract vector space and linear application will be formalized, relating them to the contents of the first block. The third block presents a factorization in linear applications that has different uses in the world of engineering. The fourth block is dedicated to more advanced concepts that take advantage of the structure of vector space with metrics.
Topic 1: Matrices and linear equations
(A) Operations with matrices. Invertible matrix.
(B) Elemental transformations in matrices.
(C) Rank of a matrix. Invertibility criterion. PAQ-reduction. Generalized Invers matrix.
(D) Resolution of systems of linear equations.
(E) Determinant of a square matrix.
Topic 2: Vector spaces and linear applications
(A) Definition of space and vector subspace. Scalar products in vector spaces. Linear independence, generators and bases. Dimension.
(B) Nucleus and image of a linear application. Composition.
(C) Vector coordinates and matrix associated with a linear application.
Topic 3: Diagonalization
(A) Characteristic polynomial. Eigenvalues.
(B) Eigenvectors associated with an eigenvector. Diagonalization of matrices.
(C) Minimum polynomial.
Topic 4: Orthogonality, normed spaces and quadratic forms.
(A) Bilinear forms and diagonalization in symmetric matrices.
(B) Singular values and SVD factoring (Singular Value Decomposition). Fitting Date.
(C) Hilbert spaces.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Solving exercises and Computer class with a mathematic programme. | 24 | 0.96 | 1, 2, 4, 5, 7 |
theory class | 26 | 1.04 | 1, 2, 3, 7 |
Type: Autonomous | |||
Computer work with Sage Math | 27 | 1.08 | 1, 5, 7 |
Learn theoretical concepts and solving exercises. | 65.5 | 2.62 | 1, 2, 5, 7 |
The subject has during the semester of 4 weekly hours grouped in blocks of 2 hours. Each of these blocks will be divided into a theoretical introduction of content and problem solving, which may be on paper or with the use of software.
To introduce the software, more time will be devoted to this part of the sessions at the beginning of the course.
During lectures or tutorials, in the last half hour of the 2-hour block, and without notice, there will be (4 times in different days) a small test that students must do individually, which will count towards evaluation.
This course will have the corresponding Moodle classroom within the UAB servers to offer complementary material. This will be the virtual platform for communication with the students.
Professors should allocate approximately 15 minutes of some class to allow their students to answer the surveys for the evaluation of teaching performance and the evaluation of the subject or module.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Final exam | 50% | 3 | 0.12 | 1, 2, 6, 7 |
Mid term exam | 35% | 2.5 | 0.1 | 1, 2, 3, 4, 5, 6, 7 |
SageMath exam | 15% | 2 | 0.08 | 1, 4, 6, 7 |
Continuous assessment:
During the course, at a time and date that will be announced beforehand, there will be a partial exam lasting two and a half hours, where the contents of the assignment achieved up to that point, both theoretical and practical, will be evaluated . . This exam will be taken individually and is non-refundable. The grade for this exam is denoted by EP
Exam type evaluation:
During the month of May, at a time and date to be fixed, there will be a computer-based practice assessment. The level achieved with the course will be assessed with the help of software with the laptop. The test will be individual. This test can be retaken during the resit date, however it must have a minimum score of 1 point out of 10 to be able to evaluate the course; otherwise the student will fail the course (see the grading section). We denote this grade between 0 and 10 by P, and remember it is mandatory to take this test since P must be greater than or equal to 1 in order to pass the course.
At the end of the course, there will be a final exam of the whole subject. Denote by E the final exam grade on 10 points.
Qualification of the subject (without resits):
If the grade E is equal to or higher than 3.5 and the grade P is equal to or higher than 1, then at this point the student has the qualification N =0.35 * EP + 0.15 * P + 0.5 * E. If the grade is higher than or equal to 5, the student passes the course with note N.
If P <1 or E <3,5 (or the student hasn't turned up at the practical exam or end of the subject) the student obtains the minimum grade between N and 4.5 points.
The student obtains a Non-evaluable in case she or he does fails to hand in exercises, does not turn up for the last two Quizzes and she or he does not turn up in any of the exams.
Repeat students will not be treated differently from the rest of the students.
Review of grades: Each evaluable activity will have a date to be reviewed, announced in good time on the day of the test or with a minimum of 24 hours after the publication of the grades.
Single assessment: Students who decide to take the single assessment will take a written test on the same day as the final exam in which the contents of the entire course will be assessed, including those contents covered in the exercises delivered. Those students will also take another test, on the same day, of practicals with a computer. These tests can be recovered on the day of the recovery exam, in the same format. The weight of the practical exam will be 15% while the rest of the qualification will correspond to the written test.
Resit exams:
Students with N<5 or E<3.5 (always with P>1) must take the make-up exam if they want to try to pass the subject, otherwise the grade will remain as described above. To be able to take the recovery exam it is imperative that P>1.
The make-up exam is an exam of the whole course with the same value as the final exam of the course, we say in the note of this make-up exam by Erec.
Final qualification of the course (for students that take the resit exam):
We denote by Nfin:=0.35*EP+0.15*P+0.5*Erec. If Erecup>3.5, the student's qualification will be Nfin. If Erecup is lower than 3.5, the student's grade will be the minimum between 4.5 and Nfin.
Annex on the qualification of the subject:
Students who have more than a 9.25 in the final qualification will have a Matricula d'Honor (MH) until reaching the limit of 5% of those enrolled. If there aremore than 5% of students above 9.25, those with the highest marks will have MH.
"Without prejudice to other disciplinary measures that are deemed appropriate, andin accordance with current academic regulations, irregularities committed by a student that may leadto a variation of the qualification will be graded with a zero (0). The activities of 'assessment graded in this way and by this procedure will not be recoverable. If it is necessary to pass any of these assessment activities to pass the subject, this subject will be suspended directly, with no opportunity to recover it in the same course. These irregularities include, among others:
- the total or partial copy of a practice, report, or any other assessment activity;
- let copy;
- present a group work not done entirely by the group members;
- present as own materials prepared by a third party, even if they are translations or adaptations, and in general works with non-original and exclusive elements of the student;
- have communication devices (such as mobile phones, smart watches, etc.) accessible during individual theoretical-practical assessment tests (exams)."
In case of discrepancy, the version that maintains validity is the version in Catalan.
Bretscher,O. "Linear Algebra with Applications", 1997, Prentice-Hall International, Inc.
Nart,E.;Xarles,X."Apunts d'àlgebra lineal", 2016, col.lecció Materials UAB, num.237.
Seasone,G"Elementary notions of Hilbert Spaces" 1991, NewYork, Dover.
Virtual Bibliography:
Bars, F.:Uns apunts de càlcul matricial i resolució de sistemes lineals. https://ddd.uab.cat/record/73660
Bars.F: Una pinzellada del polinomi mínim. https://ddd.uab.cat/record/236746
Bars, F: Espais normats i Espais de Hilbert, per a primer curs. https://ddd.uab.cat/record/236744
Masdeu, M, Ruiz, A: Apunts d'Àlgebra Lineal, https://mat.uab.cat/~masdeu/wp-content/uploads/2022/06/ApuntsAlgebraLineal.pdf
Use of SageMath with the computations inputs of the different subjects given in the course.
Name | Group | Language | Semester | Turn |
---|---|---|---|---|
(PAUL) Classroom practices | 811 | Catalan | second semester | morning-mixed |
(PAUL) Classroom practices | 812 | Catalan | second semester | morning-mixed |
(PLAB) Practical laboratories | 811 | Catalan | second semester | morning-mixed |
(PLAB) Practical laboratories | 812 | Catalan | second semester | morning-mixed |
(TE) Theory | 81 | Catalan | second semester | morning-mixed |